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Given a Finsler manifold $(M,F)$ which admits a concurrent $\\pi$-vector field $\\overline{\\varphi}$, we consider the change $\\widehat{F}(x,y)=\\frac {F^2 (x,y)} {F(x,y)-\\Phi(x,y)}$, where $\\Phi$ is the associated concurrent $\\pi$-form with $F(x,y) > \\Phi(x,y)$ for all $(x,y) \\in \\T M$. We find the condition under which the generalized $\\phi$-Matsumoto metric $\\widehat{F}$ is a Finsler metric. Moreover, the relations between the associated Finslerian geometric objects of $\\widehat{F}$ and $F$ are obtained, namely, the relations betwee"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2510.22463","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2025-10-26T00:15:47Z","cross_cats_sorted":[],"title_canon_sha256":"1c5f105cf2ecfcb08317590c6173be923085cd2c89c42538e11f6b980dc2e0d8","abstract_canon_sha256":"9823be295228060b26c2732a7b7fd1a2da11939b37aabf77faeae01f3d7a0f7d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:21:42.154505Z","signature_b64":"gqZGyNfaGdgOP7AUj8E4su04s+J5nE9RwbGRdy70rbN4LqmZUG7qrip4KfsVD2tECZe9IcJ7Xac2njuiWPfmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5311a1f05d5fc962a60ff610739dd7f34ba14029b06dffa7a3af797f256c24d","last_reissued_at":"2026-07-16T01:21:42.153473Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:21:42.153473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Generalized Matsumoto Metrics with a Special $\\pi$-form","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"A. Soleiman, Ebtsam H. Taha","submitted_at":"2025-10-26T00:15:47Z","abstract_excerpt":"We explore a generalization of Matsumoto metric intrinsically. Given a Finsler manifold $(M,F)$ which admits a concurrent $\\pi$-vector field $\\overline{\\varphi}$, we consider the change $\\widehat{F}(x,y)=\\frac {F^2 (x,y)} {F(x,y)-\\Phi(x,y)}$, where $\\Phi$ is the associated concurrent $\\pi$-form with $F(x,y) > \\Phi(x,y)$ for all $(x,y) \\in \\T M$. We find the condition under which the generalized $\\phi$-Matsumoto metric $\\widehat{F}$ is a Finsler metric. 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